Such systems are designed to operate in multiuser and often hostile environments, and are intended for a wide range of applications, including automotive applications, industrial robotics and unmanned vehicle navigation.
FIG. 1 is a block diagram of a typical microwave obstacle-detection system. The system comprises a signal generator 1 that produces a substantially continuous waveform x(t) with suitable bandwidth to provide required range resolution. The waveform x(t) may be deterministic (periodic or aperiodic), chaotic or purely random.
The system also has a microwave oscillator 2 that generates a sinusoidal signal with required carrier frequency, a modulator 3 that modulates one or more of the parameters (such as amplitude, phase, or frequency) of the carrier signal with the modulating waveform x(t), a power amplifier (PA) 4 that amplifies the modulated carrier signal to a required level, a microwave transmit antenna (TA) 5 that radiates an electromagnetic wave representing the modulated carrier signal towards an obstacle 6, a microwave receive antenna (RA) 7 that receives an electromagnetic wave reflected back by the obstacle 6, an input amplifier (IA) 8 that amplifies a signal provided by the receive antenna (RA) 7, and a coherent demodulator 9 that processes jointly the reference carrier signal supplied by the oscillator 2 and a signal supplied by the input amplifier (IA) 8 to reconstruct a time-delayed replica y(t) of the modulating waveform x(t).
The modulating waveform x(t) and its time-delayed replica y(t) are then processed jointly during a specified time interval by a suitable processor 10, such as correlator, to produce an estimate of the unknown time delay that is proportional to the distance (range) between the system and the obstacle 6.
FIG. 2 shows an example of a correlation function of a synchronous random binary waveform.
When there occurs a relative movement between a ranging system and an obstacle of interest, an electromagnetic wave reflected back by the obstacle and received by a coherent system will exhibit a Doppler frequency shift. The value ωD0 of this (angular) frequency shift can be determined from:
      ω    D0    =                    2        ⁢                                  ⁢                  υ          0                    c        ⁢          ω      0      where υ0 is the radial speed (i.e., the range rate) of a relative movement between the system and the obstacle and ω0 is the (angular) carrier frequency of a transmitted electromagnetic wave having velocity c.
The signal reflected back by a moving obstacle can be expressed as:zr(t)=γx(t−τ0)cos [(ω0+ωD0)(t−τ0)+θ]where γ is the round-trip attenuation, τ0 is the delay corresponding to the range D, ωD0 is the Doppler frequency shift, and θ is an unknown constant phase shift. Strictly speaking, the value of τ0 cannot be constant for a nonzero Doppler frequency ωD0. However, in most practical cases it is assumed that the small changes in range D, of the order of the wavelength of the carrier frequency, cannot be discerned when determining a short-time time-delay estimate. Such assumption justifies decoupling delay and Doppler frequency measurements.
A baseband signal corresponding to the received signal zr(t) has the formy(t)=x(t−τ0)cos(ωD0t+φ) where φ is an unknown phase shift.
The correlator performs the following operation
            R      xy        ⁡          (      τ      )        =            1              T        0              ⁢                  ∫        0                  T          0                    ⁢                        x          ⁡                      (                          t              -              τ                        )                          ⁢                  x          ⁡                      (                          t              -                              τ                0                                      )                          ⁢                  cos          ⁡                      (                                                            ω                  D0                                ⁢                t                            +              φ                        )                          ⁢                                  ⁢                  ⅆ          t                    where the integral is evaluated for a plurality of hypothesized time delays τmin<τ<τmax. When the observation interval T0 is much shorter than one period (2π/ωD0) of the Doppler frequency, the value of cos(ωD0tm+φ) is almost constant during T0, so that the correlation integral can be approximated by
            R      xy        ⁡          (      τ      )        ≈            1              T        0              ⁢          cos      ⁡              (                                            ω              DO                        ⁢                          t              m                                +          φ                )              ⁢                  ∫        0                  T          0                    ⁢                        x          ⁡                      (                          t              -              τ                        )                          ⁢                  x          ⁡                      (                          t              -                              τ                0                                      )                          ⁢                                  ⁢                  ⅆ          t                    where the time instant tm is taken in the middle of the observation interval T0.
When the correlation integral is calculated repeatedly for successive short processing intervals, each of duration T0, the sequence of observed correlation functions may be represented by the plot of FIG. 3. The rate of change (in time) of the correlation function Rxy(τ) will correspond to the Doppler frequency ωD0. The value of this frequency can be determined by applying some suitable form of spectral analysis.
FIG. 4 is a block diagram of a conventional correlator, comprising variable delay line 11, multiplier 12 and integrator 13, followed by a spectrum analyser 14. When the total number of successive short processing intervals is large enough, the frequency spectrum S(ω), observed at the output of the analyser, will exhibit a pronounced peak at the Doppler frequency ωD0.
FIG. 5 is a block diagram of a multichannel correlator that uses a tapped delay line 15 to cover the entire interval of hypothesized time delays, τmin<τ<τmax, in J steps of unit delay Δ using delay circuits 16. Multipliers 17 process the delayed signals with y(t) and provide the outputs to integrators 18. The required spectral analysis may be performed by a digital processor 19 implementing the Discrete Fourier Transform (DFT). The principle of operation is thus similar to that of FIG. 4.
The systems shown in FIGS. 4 and 5, and also other similar known systems, attempt to approximate the correlation integral with two parameters of interest, delay time τ and Doppler frequency ωD by combining a time sequence of correlation functions determined over a number of relatively short observation intervals T0. Because of this approximation, such systems can only provide suboptimal solutions to the problem of joint estimation of time delay and Doppler frequency.
Another prior art technique involves determining values of the following correlation integral
            R      xy        ⁡          (              τ        ,                              ω            D                    ;          φ                    )        =            1              T        0              ⁢                  ∫        0                  T          0                    ⁢                        x          ⁡                      (                          t              -              τ                        )                          ⁢                  cos          ⁡                      (                                                            ω                  D                                ⁢                t                            +              φ                        )                          ⁢                  y          ⁡                      (            t            )                          ⁢                                  ⁢                  ⅆ          t                    for the entire interval of hypothesized time delaysτmin<τ<τmax,and also for the entire interval of hypothesized Doppler frequenciesωDmin<ωD<ωDmax;the unknown phase φ should also be varied over the interval (0, 2π). In this case, values of the correlation integral, determined for some prescribed range of argument values (τ,ωD), define a two-dimensional correlation function. The specific values of arguments τ and ωD, say τ0 and ωD0, that maximise the two-dimensional correlation function provide estimates of unknown time delay and unknown Doppler frequency.